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File:3-adic integers with dual colorings.svg

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38: 518: 612: 524: 487: 529: 90: 466: 1791: 1846: 274: 570:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. 477: 424: 354: 205: 319: 1851: 64: 60: 56: 52: 48: 42: 101: 73: 210: 1831: 362:
For details on the embedding of the 3-adic integers, see Chistyakov, D. V. (1996), “Fractal geometry for images of continuous embeddings of
165:
Counter-clockwise from the right, the labeled elements are 0, 9, 3, 1, −1/8, −1/2, 1/4, −1/4, 1/2, 1/8, −1, −3, and −9. Open the SVG
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The following pages on the English Knowledge (XXG) use this file (pages on other projects are not listed):
175: 1790: 1785: 37: 576:– If you remix, transform, or build upon the material, you must distribute your contributions under the 1894: 629: 536: 279: 153: 1836: 634: 621: 109: 1357: 606: 493: 160: 1821: 157: 149: 145: 1841: 1826: 1801: 322: 152:(black points), with selected elements labeled by the corresponding character on the 96: 511:
I, the copyright holder of this work, hereby publish it under the following license:
1939: 669: 497: 357: 1227: 1218: 269:{\displaystyle \chi _{x}:\mathbb {Z} (3^{\infty })\to \mathbb {R} /\mathbb {Z} } 1847:
Knowledge (XXG):Featured picture candidates/3-adic integers with dual colorings
455: 435: 1038: 732: 1969: 1191: 1164: 1074: 1011: 741: 651: 1209: 1200: 1182: 1173: 1155: 1146: 1137: 1128: 1119: 1110: 1101: 1092: 1083: 1065: 1056: 1047: 1029: 1020: 1002: 993: 984: 975: 966: 957: 948: 939: 930: 921: 912: 903: 894: 885: 876: 867: 858: 849: 840: 831: 822: 813: 804: 795: 786: 777: 768: 759: 750: 723: 714: 705: 696: 687: 678: 660: 642: 383: 1929: 1884: 207:, and it represents the corresponding character on the Prüfer 3-group, 486: 1879: 472: 1758:
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Knowledge (XXG):Featured picture candidates/March-2012
426:, defined in Definition 3 and depicted in Figure 1.12. 1039: 733: 394: 330: 282: 213: 178: 1431:
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1192: 1165: 1075: 1012: 742: 652: 1210: 1201: 1183: 1174: 1156: 1147: 1138: 1129: 1120: 1111: 1102: 1093: 1084: 1066: 1057: 1048: 1030: 1021: 1003: 994: 985: 976: 967: 958: 949: 940: 931: 922: 913: 904: 895: 886: 877: 868: 859: 850: 841: 832: 823: 814: 805: 796: 787: 778: 769: 760: 751: 724: 715: 706: 697: 688: 679: 661: 643: 418: 388:, pages 1495–1507. The particular mapping used is 348: 313: 268: 199: 172:Each colored disc is tied to a 3-adic integer, 587:https://creativecommons.org/licenses/by-sa/3.0 89: 593:Creative Commons Attribution-Share Alike 3.0 517: 8: 360:where 0 = red, 1/3 = green, and 2/3 = blue. 553:– to copy, distribute and transmit the work 370:-adic solenoids into Euclidean spaces”, in 41:Size of this PNG preview of this SVG file: 1760: 1358:http://commons.wikimedia.org/User:Melchoir 1258: 1236: 1862:The following other wikis use this file: 1832:Talk:Fermat's Last Theorem/Archive 7 419:{\displaystyle \Upsilon _{s}^{(\infty )}} 404: 399: 393: 349:{\displaystyle \mathbb {R} /\mathbb {Z} } 342: 341: 336: 332: 331: 329: 287: 281: 262: 261: 256: 252: 251: 239: 228: 227: 218: 212: 191: 187: 186: 177: 1606:145cd52fc13e6211266c0c76440f4124d45ea534 1819: 1733: 1717: 1696: 1680: 1659: 1643: 1604: 1588: 1570: 1554: 1534: 1518: 1498: 1482: 1464: 1448: 1428: 1412: 1392: 1376: 1309: 1293: 1276: 1273: 1254: 1247: 627:This image has been assessed using the 134:3-adic integers with dual colorings.svg 200:{\displaystyle x\in \mathbb {Z} _{3}} 7: 540:Attribution-Share Alike 3.0 Unported 372:Theoretical and Mathematical Physics 1749: 528: 523: 376: 169:to get tooltips on group elements. 1267: 1261: 617: 514: 510: 491: 470: 408: 396: 240: 138: 121: 71: 1266: 1252: 610: 564:Under the following conditions: 535:This file is licensed under the 527: 522: 516: 485: 464: 88: 31: 21: 1970:Wikipedysta:P-adyczny/brudnopis 1537:Wikimedia Commons quality image 1249: 314:{\displaystyle \chi _{x}(q)=xq} 139: 14: 1976:Usage on simple.wikipedia.org 1248: 411: 405: 299: 293: 248: 245: 232: 26: 1: 1501:original creation by uploader 1274:Items portrayed in this file 2023: 1996:Usage on zh.wikipedia.org 1986:Usage on uk.wikipedia.org 1966:Usage on pl.wikipedia.org 1956:Usage on no.wikipedia.org 1946:Usage on nl.wikipedia.org 1936:Usage on ko.wikipedia.org 1926:Usage on ja.wikipedia.org 1916:Usage on hu.wikipedia.org 1906:Usage on fr.wikipedia.org 1891:Usage on fa.wikipedia.org 1876:Usage on es.wikipedia.org 1866:Usage on bg.wikipedia.org 1521:Commons quality assessment 578:same or compatible license 1750: 445: 16: 2005:Knowledge (XXG):优良条目/p进数 1251: 671:беларуская (тарашкевіца) 630:Quality image guidelines 544: 167:directly in your browser 95:This is a file from the 1807: 1786:08:48, 17 February 2012 451: 441: 434: 431: 374:, volume 109, issue 3, 131: 99:. Information from its 420: 350: 315: 270: 201: 102:description page there 734:Schweizer Hochdeutsch 421: 351: 316: 271: 202: 154:Pontryagin dual group 1618:determination method 633:and is considered a 392: 328: 280: 211: 176: 65:2,048 × 2,048 pixels 61:1,024 × 1,024 pixels 1040:português do Brasil 559:– to adapt the work 496:was created with a 415: 163:) (colored discs). 47:Other resolutions: 1837:Talk:P-adic number 1336:Wikimedia username 1323:author name string 416: 395: 384:10.1007/BF02073866 366:-adic numbers and 346: 311: 266: 197: 1950:P-adische analyse 1858:Global file usage 1810: 1415:copyright license 1260: 1246: 1245: 1240: 461: 460: 387: 117: 116: 97:Wikimedia Commons 32:Global file usage 2014: 1990:P-адичний аналіз 1885:Análisis p-ádico 1798: 1738: 1701: 1664: 1627: 1622: 1466:17 February 2012 1379:copyright status 1360: 1355: 1345: 1340: 1330: 1327: 1241: 1013:Norfuk / Pitkern 887:Bahasa Indonesia 614: 613: 607: 600: 597: 594: 591: 588: 580:as the original. 537:Creative Commons 531: 530: 526: 525: 520: 519: 489: 480: 468: 447: 437: 436:17 February 2012 425: 423: 422: 417: 414: 403: 386: 380: 375: 373: 355: 353: 352: 347: 345: 340: 335: 320: 318: 317: 312: 292: 291: 275: 273: 272: 267: 265: 260: 255: 244: 243: 231: 223: 222: 206: 204: 203: 198: 196: 195: 190: 143: 135: 129: 113: 92: 91: 85: 79: 68: 57:768 × 768 pixels 53:480 × 480 pixels 49:240 × 240 pixels 43:600 × 600 pixels 2022: 2021: 2017: 2016: 2015: 2013: 2012: 2011: 1920:P-adikus számok 1910:Nombre p-adique 1856: 1822:P-adic analysis 1818: 1811: 1804: 1796: 1752: 1751: 1748: 1747: 1746: 1745: 1744: 1743: 1742: 1741: 1739: 1736: 1726: 1725: 1724: 1722: 1711: 1710: 1709: 1708: 1707: 1706: 1705: 1704: 1702: 1699: 1689: 1688: 1687: 1685: 1674: 1673: 1672: 1671: 1670: 1669: 1668: 1667: 1665: 1662: 1652: 1651: 1650: 1648: 1637: 1636: 1635: 1634: 1633: 1632: 1631: 1630: 1629: 1628: 1623: 1620: 1611: 1610: 1609: 1607: 1597: 1596: 1595: 1593: 1582: 1581: 1580: 1579: 1578: 1577: 1576: 1575: 1573: 1563: 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654: 645: 641: 638: 626: 611: 603: 602: 601: 598: 595: 592: 589: 586: 585: 543: 532: 513: 512: 507: 502: 501: 483: 482: 476: 462: 427: 390: 389: 382: 371: 326: 325: 283: 278: 277: 235: 214: 209: 208: 185: 174: 173: 150:3-adic integers 133: 126: 119: 118: 107: 106: 105:is shown below. 81: 77: 70: 69: 46: 12: 11: 5: 2020: 2018: 2010: 2009: 2008: 2007: 2002: 1994: 1993: 1992: 1984: 1983: 1982: 1974: 1973: 1972: 1964: 1963: 1962: 1954: 1953: 1952: 1944: 1943: 1942: 1934: 1933: 1932: 1924: 1923: 1922: 1914: 1913: 1912: 1904: 1903: 1902: 1900:آنالیز پی-ادیک 1897: 1889: 1888: 1887: 1882: 1880:Número p-ádico 1874: 1873: 1872: 1870:P-адично число 1860: 1859: 1855: 1854: 1849: 1844: 1839: 1834: 1829: 1824: 1816: 1815: 1814: 1809: 1808: 1806: 1802: 1799: 1793: 1788: 1783: 1779: 1778: 1775: 1772: 1769: 1766: 1763: 1756: 1755: 1740: 1734: 1732: 1731: 1730: 1729: 1728: 1727: 1723: 1718: 1716: 1715: 1714: 1713: 1712: 1703: 1697: 1695: 1694: 1693: 1692: 1691: 1690: 1686: 1681: 1679: 1678: 1677: 1676: 1675: 1666: 1660: 1658: 1657: 1656: 1655: 1654: 1653: 1649: 1644: 1642: 1641: 1640: 1639: 1638: 1616: 1615: 1614: 1613: 1612: 1608: 1605: 1603: 1602: 1601: 1600: 1599: 1598: 1594: 1589: 1587: 1586: 1585: 1584: 1583: 1574: 1571: 1569: 1568: 1567: 1566: 1565: 1564: 1560: 1555: 1553: 1552: 1551: 1550: 1549: 1540: 1535: 1533: 1532: 1531: 1530: 1529: 1528: 1524: 1519: 1517: 1516: 1515: 1514: 1513: 1504: 1499: 1497: 1496: 1495: 1494: 1493: 1492: 1488: 1485:source of file 1483: 1481: 1480: 1479: 1478: 1477: 1468: 1465: 1463: 1462: 1461: 1460: 1459: 1458: 1454: 1449: 1447: 1446: 1445: 1444: 1443: 1434: 1429: 1427: 1426: 1425: 1424: 1423: 1422: 1418: 1413: 1411: 1410: 1409: 1408: 1407: 1398: 1393: 1391: 1390: 1389: 1388: 1387: 1386: 1382: 1377: 1375: 1374: 1373: 1372: 1371: 1349: 1348: 1334: 1333: 1321: 1320: 1319: 1318: 1317: 1313: 1310: 1308: 1307: 1306: 1305: 1304: 1303: 1299: 1294: 1292: 1291: 1290: 1289: 1288: 1282: 1277: 1275: 1272: 1271: 1270: 1269: 1268: 1257: 1256: 1253: 1250: 1244: 1243: 950:Lëtzebuergesch 618: 615: 584: 583: 582: 581: 571: 562: 561: 560: 554: 547:You are free: 534: 533: 515: 509: 508: 506: 503: 484: 463: 459: 458: 453: 449: 448: 443: 439: 438: 433: 429: 428: 413: 410: 407: 402: 398: 344: 339: 334: 310: 307: 304: 301: 298: 295: 290: 286: 264: 259: 254: 250: 247: 242: 238: 234: 230: 226: 221: 217: 194: 189: 184: 181: 161:Prüfer 3-group 136: 127: 125: 122: 120: 115: 114: 93: 83: 82: 40: 36: 35: 34: 29: 24: 19: 13: 10: 9: 6: 4: 3: 2: 2019: 2006: 2003: 2001: 1998: 1997: 1995: 1991: 1988: 1987: 1985: 1981: 1980:P-adic number 1978: 1977: 1975: 1971: 1968: 1967: 1965: 1961: 1958: 1957: 1955: 1951: 1948: 1947: 1945: 1941: 1938: 1937: 1935: 1931: 1928: 1927: 1925: 1921: 1918: 1917: 1915: 1911: 1908: 1907: 1905: 1901: 1898: 1896: 1893: 1892: 1890: 1886: 1883: 1881: 1878: 1877: 1875: 1871: 1868: 1867: 1865: 1864: 1863: 1857: 1853: 1850: 1848: 1845: 1843: 1842:User:Melchoir 1840: 1838: 1835: 1833: 1830: 1828: 1827:P-adic number 1825: 1823: 1820: 1812: 1805: 1800: 1794: 1792: 1789: 1787: 1784: 1781: 1780: 1776: 1773: 1770: 1767: 1764: 1762: 1761: 1759: 1753: 1721: 1684: 1647: 1626: 1619: 1592: 1572:image/svg+xml 1558: 1538: 1522: 1502: 1486: 1452: 1432: 1416: 1396: 1380: 1359: 1352: 1344: 1337: 1324: 1297: 1280: 1242: 1239: 1235: 1231: 1226: 1222: 1217: 1213: 1208: 1204: 1199: 1195: 1190: 1186: 1181: 1177: 1172: 1168: 1163: 1159: 1154: 1150: 1145: 1141: 1136: 1132: 1127: 1123: 1118: 1114: 1109: 1105: 1100: 1096: 1091: 1087: 1082: 1078: 1073: 1069: 1064: 1060: 1055: 1051: 1046: 1042: 1037: 1033: 1028: 1024: 1019: 1015: 1010: 1006: 1001: 997: 995:Bahasa Melayu 992: 988: 983: 979: 974: 970: 965: 961: 956: 952: 947: 943: 938: 934: 929: 925: 920: 916: 911: 907: 902: 898: 893: 889: 884: 880: 875: 871: 866: 862: 857: 853: 848: 844: 839: 835: 830: 826: 821: 817: 812: 808: 803: 799: 794: 790: 785: 781: 776: 772: 767: 763: 758: 754: 749: 745: 740: 736: 731: 727: 722: 718: 713: 709: 704: 700: 695: 691: 686: 682: 677: 673: 668: 664: 659: 655: 650: 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File
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File:3-adic integers with dual colorings.svg
600 × 600 pixels
240 × 240 pixels
480 × 480 pixels
768 × 768 pixels
1,024 × 1,024 pixels
2,048 × 2,048 pixels
Original file
Wikimedia Commons
description page there
You can help
compact group
3-adic integers
Pontryagin dual group
discrete
Prüfer 3-group
directly in your browser
circle group
color wheel
DOI
10.1007/BF02073866
Melchoir

SVG
valid

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